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This paper describes the extension of a
recently developed numerical solver for the Landau-Lifshitz
Navier-Stokes (LLNS) equations to binary mixtures in three
dimensions. The LLNS equations incorporate thermal fluctuations into
macroscopic hydrodynamics by using white-noise fluxes. These
stochastic PDEs are more complicated in three dimensions due to the
tensorial form of the correlations for the stochastic fluxes and in
mixtures due to couplings of energy and concentration fluxes (e.g.,
Soret...
Under the key assumption of finite -variation, , of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), resp. , we recover and extend the respective results of (Trans. Amer. Math. Soc.361 (2009) 2689–2718) and (Ann. Inst. Henri Poincasé Probab. Stat.48(2012) 518–550). In particular, we establish an a.s. rate , any , for Wong–Zakai and Milstein-type...
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